Conventionally, a correlative method is used as a technique for evaluating the similarity of two signals. The correlative method is also referred to as matched filter.
In this correlative method, correlation of two signals is taken while the time between the two signals is shifted, and the similarity can be evaluated by a correlation value at the time when the maximum correlation is taken. The correlative method is an optimum comparison technique because it provides the maximum signal-to-noise ratio between one signal and the other signal. Particularly when a pattern to be detected is known, the correlative method is used as a method for detecting pattern from an observation signal tainted by noise in a wide variety of fields such as signal detection, acoustic processing, image processing, and radar technology.
Meanwhile, in the case of evaluating the similarity between two observation signals from an unknown original signal, or when signals and noise are unsteady, the correlative method might be dominated by unsteadiness of noise components and cannot necessarily be an appropriate comparison technique. Such a case will now be described in detail.
FIGS. 1A and 1B show two observation signals A and B including similar signals. The similar signals included in the observation signals have a shift of 300 samples and a difference in amplitude of approximately 1.5 times. The individual observation signals are tainted by unsteady noise signals. In sections indicated by arrows in FIGS. 1A and 1B, a high signal-to-noise ratio is observed and the two signals are relatively similar to each other. However, in the other parts, there are many noise signals and the two signals are hardly similar to each other. As a matter of course, which section has a high signal-to-noise ratio, that is, which section is suitable for similarity evaluation, is not known in advance.
Of such observation signals, a part consisting of samples 0 to 500 the observation signal A is used as a template and its correlation value with the observation signal B is calculated by the correlative method. The result is shown in FIG. 1C. As indicated by an arrow in FIG. 1C, a peak of correlation is observed near a point where the quantity of translation is 300 samples. However, this peak is not significantly larger than the other peaks and its absolute value is approximately 0.3, which is not high enough. In this manner, with the correlative method, the similarity between observation signals with unsteady signals and noise as described above cannot be evaluated properly.